A Computational Study of Silver Doped CdSe Quantum Dots

Due to quantum dot’s ability to emit photons when subjected to light of sufficient energy, they have become optimal candidates for biomedical research and for optoelectronic applications. Fascination towards quantum dots arises from the fact that their properties are easily fine-tuned through a variety of different techniques. Electronic doping is a popular technique used to control the properties of quantum dots through the addition of different elements. Via density functional theory calculations, this work investigated how the structural energies and HOMO-LUMO gaps were altered by the addition of impurity atoms. First, interstitial and substitutional doping styles were investigated at 0 K for a CdSe quantum dot that contained a single Ag+ impurity ion, and it was concluded that the interstitial doping style was more structurally favourable than substitutional doping. In addition, different dopant locations were analyzed and it was determined that interstitially doped structures with Ag+ ions in surface site locations were approximately 1 eV more structurally favourable than structures with dopant ions placed midway in the structure and at the core. To maintain charge neutrality after the addition of a Ag+ ion, a Cl- ion was added to the surface and it was determined that the closer the two atoms were on the surface the more structurally stable the quantum dot was at 0 K. Also, the HOMO-LUMO gaps for those structures were larger by approximately 0.5 eV compared to the structures where the two atoms were placed farthest apart on the surface. At a finite temperature value of 333 K, there were no trends visible between the HOMO-LUMO gaps, structural energies, and the distance between the 2 atoms. It was however concluded that all doped structures were more energetically favourable than their undoped counterpart at both temperature values of 0 and 333 K

Toeplitz Operators on Locally Compact Abelian Groups

Given a function (more generally, a measure) on a locally compact Abelian group, one can define the Toeplitz operators as certain integral transforms of functions on the dual group, where the kernel is the Fourier transform of the original function or measure. In the case of the unit circle, this corresponds to forming a matrix out of the Fourier coefficients in a particular way. We will study the asymptotic eigenvalue distributions of these Toeplitz operators

A Combinatorial Approach to Hyperharmonic Numbers

Hyperharmonic numbers arise by taking repeated partial sums of harmonic numbers. These numbers can be expressed in terms of r-Stirling numbers, leading to combinatorial interpretations of many interesting identities

Unital Dilations of Completely Positive Semigroups

Dilations of completely positive semigroups to endomorphism semigroups have been studied by numerous authors. Most existing dilation theorems involve a non-unital embedding, corresponding to the embedding of $B(H)$ as a corner of $B(K)$ for Hilbert spaces $H \subset K$. A 1986 paper of Jean-Luc Sauvageot shows how to achieve a unital dilation, but does not specify how to do so while also preserving continuity properties of the original semigroup. This thesis further develops Sauvageot's dilation theory in order to establish the existence of continuous unital dilations, and to explore connections with free probability.Comment: 171 pages. Ph. D. thesis; upon graduation, will be published by ProQuest in cooperation with The University of Iow

Asymptotic-lp Banach Spaces and the Property of Lebesgue

The primary contribution of this work is to nearly characterize the Property of Lebesgue for Banach spaces that behave in a global asymptotic sense like lp. This generalizes a number of individual results that are collected by Russell Gordon in his 1991 survey article among other notable consequences and also raises the possibility of characterizing the Property of Lebesgue for more general Banach spaces in terms of their local asymptotic structurCes

Alexander Polynomials of Tunnel Number One Knots

Every two-bridge knot or link is characterized by a rational number p/q, and has a fundamental group which has a simple presentation with only two generators and one relator. The relator has a form that gives rise to a formula for the Alexander polynomial of the knot or link in terms of p and q [15]. Every two-bridge knot or link also has a corresponding “up down” graph in terms of p and q. This graph is analyzed combinatorially to prove several properties of the Alexander polynomial. The number of two-bridge knots and links of a given crossing number are also counted

On the Incompatibility of Political Virtue and Judicial Review: A Neo-Aristotelean Perspective

Part I of this essay outlines a neo-Aristotelean theory of political virtue, an instance of virtue generally, that serves as the basis of excellent citizenship in the polis. As such, political virtue contributes its share to the achievement of eudaimonia, or the fulfillment of an individual’s natural, human function. In fact, political virtue is especially important because people are political beings, i.e. they seek the good most comprehensively in the context of association with others. Therefore, Aristotle describes politics as the master science of the supreme good, because politics orders the community of the polis and thereby establishes the norms that shape people’s lives. The theory of political virtue outlined here is not prominently or even explicitly presented in Aristotle’s Nicomachean Ethics. However, the theory is a faithful interpretation, in that it is clearly implied by (or at least logically derived from) his most basic ideas. Prominent among them is the idea that the achievement of eudaimonia requires not only cultivation of virtuous dispositions, but action motivated by virtuous dispositions and guided by practical reason (phronesis). As a result, the achievement of eudaimonia depends, in part, upon engagement in ethically significant activity that contributes directly to the shape of the political community in which one lives. Part II asks whether this theory of political virtue is compatible with strong judicial review, i.e., the form of review that empowers courts to strike down legislation duly enacted by democratically chosen representative bodies. Since the theory of political virtue requires consensual and continuous decision-making, it is found incompatible with strong judicial review as a preliminary matter. In a more extended analysis, it is also found incompatible with both a pluralist-democratic defense of strong judicial review and a popular sovereignty defense, advocating strong judicial review based on originalist interpretation of the Constitution. From the neo-Aristotelean perspective, the former fails to appreciate the qualitative uniqueness of majoritarian representation as the embodiment of morally significant action. The latter fails to appreciate the importance of continuous political activity for the attainment of eudaimonia. As a result, the neo-Aritotelean theory of political virtue appears to interpose a genuinely normative objection to strong judicial review from the standpoint of virtue ethics

Unital Dilations of Completely Positive Semigroups: From Combinatorics to Continuity

Using ideas due to Jean-Luc Sauvageot, we prove the existence of a continuous unital dilation of a CP$_0$-semigroup on a separable W$^*$-algebra. This paper presents the material in the author's Ph. D. thesis (arXiv.org:1304.0134.pdf) with some generalizations and an improved exposition.Comment: 69 pages. Submitted to Memoirs of the AM